No, this would not be helpful.
The "people need to scared in be order to act" claim is mostly advanced by journalists, and to a lesser extent by pandering politicians. Not scientists.
To better address ("solve" is not a very accurate verb in this case) the downsides of climate change, an informed public is more likely to support sensible approaches than a fearful one.
In any event, what is important to realize is that the scientific realities do not depend on psychological states or ideological preferences.
One of the biggest roadblocks to taking sensible steps in response to scientific conclusions about carbon emissions and climate change, and its effects, is that most analogies don't work very well. As Margaret Thatcher observed over a quarter century ago, global warming is a "new factor" for human societies. This large scale unrepeatable "geophysical experiment" is going forward, fear or no fear, and the costs of action have been rising along with the costs of inaction, and it is a long term problem whereas fear is a short term emotion.
A non fit for sure.